Inorganic chemistry

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Calculating the Frequency and Wavelength of an Electromagnetic Wave,.

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Calculating the number of atoms in a given amount of a compound.

Calculating the energy of a photon. Assistance Lecturer Amjad Ahmed Jumaa

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1

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Calculating the number of atoms in a given amount of a compound:

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convert from grams of compound to moles of a particular atom to number of atoms. Let's try an example.

Example: How many carbon atoms are present in (50.3 g) of (C 2 H 6 ).

Solution: We started this problem in the above example, when we calculated the moles of ethane in (50.3 g ethane). To continuo, we need two additional conversion factors. One should represent the mole ratio between moles of( C ) atoms and moles of ethane molecules. The other conversion factor needed is Avogadro's number.

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Step(1): the two conversion factors needed are:

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You should come up with the following strategy:

Grams of C

2

H

6

→ moles of C

2

H

6

→ moles of C → atoms of C. Step (2): ? C atoms = 50.3 g C

2

H

6

x x

= 2.01 x 10

24

C atom.

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Calculating the frequency and wavelength of an electromagnetic wave: All types of electromagnetic radiation move through a vacuum at a speed of about (3.00 x 10 8 m/s), which is called the speed of light( c), speed is an important property of a wave traveling through space and is equal to the product of the wavelength and the frequency of the wave. For electromagnetic waves : c = λv …………………….. (1).

Equation (1) can be rearranged as necessary to solve for either the wavelength (λ) or the frequency (v). Example: A certain (AM) radio station broadcasts at a frequency (6.00 x 10 2 What is the wavelength of these radio wave in meters. kHz).

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Solution: Step(1): solve the equation (1) algebraically for the wavelength (λ).

c = λv ……………………(2) Step (2): since the speed of light has units of (m/s). We must convert the frequency from units of (kHz) to (Hz)(s -1 ).

6.00 x 10 2 kHz x = 6.00 x 10 5 Hz = 6.00 x 10 5 s -1 .

Step (3): calculate the value of (λ) by substituting the known quantities into equation (2). λ = = 5.00 x 10 2 m.

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Example (2): What is the frequency of light that has a wavelength of (665) (nm). Solution: Step (1): solve equation (1) algebraically for the frequency (v).

c = λv …………………..(3) Step (2): since the speed of light has units of (m/s). we must convert the wavelength from units of (nm) to (m). 665 nm x = 6.65 x 10 -7 m. Step (3): calculate the value of (v) by substituting the known quantities into equation (3).

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v = = 4.51 x 10 14 s -1 = 4.51 x 10 14 Hz

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Calculating the energy of a photon:

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atoms and molecules could emit( or absorb) energy only in discrete quantities.

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Planck gave the name (quantum) to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy (E) of a single quantum of energy is given by: E = hν …………………..(4) h is Planck's constant = 6.63 x10 -34 ν is the frequency of radiation. J.s

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Example: The yellow light given off by a sodium vapor lamp has a wavelength of (589nm), what is the energy of a single photon of this radiation. Solution: Step (1): you are given wavelength in this problem. Equation (4) shows the relationship between energy and frequency. However, there is a relationship between frequency and wavelength (see equation 3).

Substituting for the frequency in equation (4), we have: ………5 Step (2): since the speed of light is in units of (m/s), we must convert the wavelength from units of (nm) to (m).

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x = 5.89 x 10 -7 m. Step (3): Calculate the value of (E) by substituting the known quantities into equation (5). E = = 3.38 x 10 -19 J.

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